Rotationally inelastic scattering of CD 3 and CH 3 with He Tká, … · 2015. 5. 31. · Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging

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Rotationally inelastic scattering of CD3 and CH3 with He

Tká, Ondej; Sage, Alan G; Greaves, Stuart J; Orr-Ewing, Andrew J.; Dagdigian, Paul J; Ma,Qianli; Alexander, Millard HPublished in:Chemical Science

DOI:10.1039/C3SC52002A

Publication date:2013

Link to publication in Heriot-Watt Research Gateway

Citation for published version (APA):Tká, O., Sage, A. G., Greaves, S. J., Orr-Ewing, A. J., Dagdigian, P. J., Ma, Q., & Alexander, M. H. (2013).Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data withquantum scattering calculations. Chemical Science, 4, 4199-4211. 10.1039/C3SC52002A

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Rotationally inelastic scattering of CD3 and CH3 with He:comparison of velocity map-imaging data withquantum scattering calculations†

Ondřej Tkáč,a Alan G. Sage,a Stuart J. Greaves,b Andrew J. Orr-Ewing,*a

Paul J. Dagdigian,*c Qianli Mac and Millard H. Alexanderd

Rotationally inelastic scattering of methyl radicals (CD3 and CH3) in collisions with helium is examined by a

combination of velocity map imaging experiments and quantum scattering calculations. In the

experiments a beam of methyl radicals seeded in Ar intersects a beam of He atoms at 90� at a collisionenergy of 440 � 35 cm�1 (CD3 + He) or 425 � 35 cm�1 (CH3 + He). The methyl radicals are preparedphotolytically in a gas expansion that cools them to 15 K, giving a distribution over a small number of

initial (low) rotational angular momentum states. By resonance-enhanced multi-photon ionization

detection, we obtain velocity map images which are specific to a single rotational angular momentum

quantum number n0 of the methyl radicals, but averaged over a small subset of the projection quantumnumber k0. We extract resolved angular scattering distributions for n0 ¼ 2–9 (for CD3). We comparethese to predictions of scattering calculations performed based on a recent potential energy surface

[P. J. Dagdigian and M. H. Alexander, J. Chem. Phys. 2011, 135, 064306] in which the methyl radical was

fixed at its equilibrium geometry. The fully (n, k) / (n0, k0) resolved differential cross sections obtainedfrom the calculations, when combined in weighted sums over initial (n, k) levels corresponding to the

15 K experimental radical temperature, and final k0 levels that are not resolved in the spectroscopicdetection scheme, show excellent agreement with the experimental measurements for all final states

probed. This agreement gives confidence in the calculated dependence of the scattering on changes in

both the n and k quantum numbers.

Introduction

Themethyl radical plays an important role in the combustion ofhydrocarbons,1,2 chemical vapour deposition (CVD) of diamondlms,3 and in the chemistry of the atmospheres of the outerplanets in the solar system.4 In addition, CH3 has been detectedin the interstellar medium via its infra-red emission bands.5

Observation of methyl radicals in the upper atmospheres ofSaturn6 and Neptune7 indicates it is a reactive intermediate inthe hydrocarbon photochemistry of these planets: methylradicals are created by vacuum ultraviolet photodissociation of

methane, and the self-recombination reaction is believed to bethe only photochemical source of ethane. The atmospheres ofgiant planets such as Saturn and Neptune are composed mainlyof molecular hydrogen and helium, with trace amounts of othersubstances. Therefore, photochemically generated methylradicals will undergo elastic and inelastic collisions with He andH2 before reactive loss, with reaction cross sections that candepend on the internal energy of the radicals.

The inelastic scattering of labile free radicals using molec-ular beams and laser spectroscopic techniques was reviewed inthe mid 1990s.8–10 However, considerable advances have beenmade since then using methods such as ion imaging11 andvelocity map imaging (VMI)12 with laser spectroscopic detectionof the nal levels. Most of these experimental studies haveconcentrated on scattering dynamics of diatomic radicals, withspectroscopic probes used to measure state-resolved integralcross sections (ICSs), and more recently differential crosssections (DCSs). The most extensively studied free radicals havebeen NO13–24 and OH,25–33 the latter because of its important rolein atmospheric chemistry, astrochemistry and combustion.Sarma et al.34 used VMI to obtain fully quantum-state-speciedproduct angular distributions for OH scattered by He and Ar,and VMI methods were also used to study collision induced

aSchool of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, UK.

E-mail: [email protected] of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh,

EH14 4AS UK. E-mail: [email protected] of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218-

2685, USA. E-mail: [email protected] of Chemistry and Biochemistry, Institute for Physical Science and

Technology, University of Maryland, College Park, Maryland 20742-2021, USA.

E-mail: [email protected]

† Electronic supplementary information (ESI) available: The ESI contains furtherdetails of the experiments and additional plots of computed DCSs in support ofthe main text. See DOI: 10.1039/c3sc52002a

Cite this: Chem. Sci., 2013, 4, 4199

Received 17th July 2013Accepted 15th August 2013

DOI: 10.1039/c3sc52002a

www.rsc.org/chemicalscience

This journal is ª The Royal Society of Chemistry 2013 Chem. Sci., 2013, 4, 4199–4211 | 4199

Chemical Science

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alignment35 and orientation36 in NO – Ar scattering. Radical –radical scattering studies are rarer, but Kirste et al.37 recentlyreported state-to-state ICSs for collisions of Stark deceleratedOH with NO.

Nevertheless, measurements of DCSs for inelastic scatteringof free radicals other than NO are rare, and to the best of ourknowledge have not been reported for reactive radicals largerthan diatomics. Macdonald and Liu,38,39 and Lai et al.40 exam-ined the inelastic scattering of the linear NCO radical with Heand Ar, respectively, but concentrated on ICSs for spin–orbitconserving and spin–orbit changing collisions. ICSs have alsobeen reported for rotationally inelastic collisions of NH2 withHe.41 Greater attention has been paid to the inelastic scatteringof closed-shell triatomic and polyatomic molecules, as illus-trated by determinations of DCSs for scattering of ammonia42–44

and deuterated ammonia45 with rare gases and molecularhydrogen, and for water with helium46 and hydrogen.47

Along with advances in experimental techniques, there havebeen many quantum scattering calculations of ICSs, and alsoDCSs, employing high-quality potential energy surfaces (PESs).These have mostly concerned collisions of diatomic and stablepolyatomic molecules.14,18,21,25–28,30–33,42,46–48 Dagdigian49 recentlyreviewed work on quantum scattering calculations of collisionalrotational and vibrational energy transfer in small hydrocarbonintermediates and highlighted studies involving methylene(CH2)50,51 and methyl.52,53 The pathways for energy transfer incollisions of a polyatomic are more complicated than for colli-sions of a diatomic molecule. There is only one type of anisot-ropy in an atom–diatom interaction, namely the difference ininteraction energy for end-on vs. side-on approach. By contrast,for collisions of a nonlinear polyatomic molecule there are twotypes of anisotropies, corresponding to approach of the colli-sion partner in or perpendicular to the molecular plane.

Dagdigian and Alexander54 recently investigated rotationalenergy transfer of methyl in collisions with a helium atomthrough quantum scattering calculations on a computed PES.This PES was calculated with a coupled-cluster method thatincludes all single and double excitations, as well as perturba-tive contributions of connected triple excitations [RCCSD(T)].Because of the anisotropy of the PES due to the repulsion of theHe atom by the three H atoms on methyl, a strong propensitywas found for Dk ¼ �3 transitions, where k is the body-frameprojection of the rotational angular momentum n.

Ma et al.53 extended this work to the study of the vibrationalrelaxation of the n2 mode of methyl by a He atom. Vibrationalrelaxation was found to be nearly two orders of magnitude lessefficient than pure rotational relaxation. The vibrational relax-ation rate also depends strongly upon the rotational quantumnumbers n and k. Although methyl has an unpaired electron,these calculations53,54 ignored the electron spin. The depen-dence of the cross sections on the spin can be determined in astraightforward manner by assuming that it is a spectatorduring the collision.49

In the present work DCSs for collisions of CH3 and CD3 withhelium are determined experimentally through the use ofcrossed molecular beam (CMB) and VMI methods. Themeasured DCSs are compared with quantum scattering

calculations that use the computed PESs mentioned above.53,54

Comparison between experiment and theory at the level of state-resolved DCSs provides a critical test of the inuence of bothshort-range repulsive and long-range attractive intermolecularinteractions. Anticipating this comparison, we nd excellentagreement between the measured and computed state-to-stateDCSs. This conrms the accuracy of the computed PES.

This paper is organized as follows: Method Sections A and Bdescribe the details of the experimental determination of theangular distributions. Method Sections C and D present,respectively, a brief description of the rotational levels of CH3and CD3, specically the different nuclear spin modications,and the spectroscopic intricacies of the detection scheme.Section E describes the quantum scattering calculations.Results Sections A and B present and compare the measuredand theoretical cross sections for collision of CD3 and CH3 withHe, respectively. Discussion and Conclusions sections thenfollow.

MethodA. Experimental apparatus

Experimental measurements were carried out using a newlyconstructed, compact crossed molecular beam machine withvelocity map imaging detection, based on the design of Streckerand Chandler.55 Pulsed molecular beams of jet-cooled methylradicals (either CD3 or CH3) and helium crossed at 90� in a highvacuum chamber, and the velocities of the scattered methylradicals were imaged following resonance enhanced multi-photon ionization (REMPI) with rotational level resolution. Theresultant images were corrected by density to ux conversionprior to analysis of angular dependences to derive quantum-state-resolved differential cross sections. A schematic diagramof the top and side view of the instrument is depicted in Fig. 1,and the component parts are described in greater detail below.

Molecular beams were formed by supersonic expansion ofgas samples through a pair of pulsed valves (General ValveSeries 9), and the expansions were collimated by skimmers. Thepulsed valves operated at 10 Hz repetition rate, the nozzlediameters were 0.8 mm, and the skimmer orices were 1 mm

Fig. 1 Schematic (a) top and (b) side views of the experimental miniaturecrossed molecular beam machine. (c) The design of the ion optics for DC sliceimaging. The red lines represent the electric field lines of force created by theelectrodes with applied voltages corresponding to experimental operation. Thedimensions of key elements in the scattering region are given in the main text.

4200 | Chem. Sci., 2013, 4, 4199–4211 This journal is ª The Royal Society of Chemistry 2013

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diameter. The nozzle-skimmer distances could be adjusted inthe range 0.2 cm to 4.3 cm, and for the current experimentswere selected to be 3.2 cm. The distance from each skimmer tothe scattering centre was 3.7 cm. The source chambers wereevacuated by a turbomolecular pump (Edwards nEXT300D). Thetwo skimmed beams propagated horizontally and crossed at a90� intersection angle. The gas ows in both beams passedthrough the scattering region and were directed straight intotwo additional turbomolecular pumps (Pfeiffer HiPace 80). Atypical base pressure for the scattering chamber was

ion signal and any background contributions from the inter-action of the probe laser with the primary beam. The desiredscattering signal was then obtained by subtraction of thebackground image from the total signal image.

B. Density-to-ux transformation

A Newton diagram for inelastic scattering of CD3 with He isshown in Fig. 2 and illustrates the laboratory frame velocities ofCD3 [vCD3 ¼ 550 � 30 m s�1], and helium [vHe ¼ 1710 � 80 ms�1], and the pre- and post-collision centre-of-mass (CM) framevelocities of the methyl radical uCD3 and u

0CD3 , respectively. The

CM-frame scattering angle q is dened as the angle between theCM-frame velocities of CD3 before and aer a collision. Analysisof experimental images requires a density-to-ux trans-formation because the detection efficiency of the scatteredproducts depends on their laboratory frame velocity. Thisdetection bias leads to an asymmetry in the measured imageswith respect to the relative velocity vector (dashed line in Fig. 2).

To correct the images for this detection bias, we employ themethod of Monte Carlo simulation of the experiment, using amodication of the computer program of Eyles and Brouard.61

This code simulates an instrument function that determines arelative detection efficiency of scattered molecules that dependson their nal laboratory frame velocity. The changes made tothe Monte Carlo program include simulation of slicing of thecentral part of the Newton sphere. For reliable use of thesimulation program, values for various parameters character-izing the experimental apparatus were carefully determined.These parameters included the speed and angular divergencedistributions, temporal proles, and spatial widths of the twomolecular beams, as well as the temporal prole, Rayleighrange and beam waist of the focused probe laser. By sampling�2 � 108 sets of initial conditions from the distributions ofmolecular beam and laser beam properties, the Monte Carloprogram was used to simulate the instrument function. As willbe discussed in Section D, the k projection number is notresolved in the REMPI spectra of methyl radicals. A set ofinstrument functions was therefore simulated for individual kprojection numbers and each was weighted according to the2-photon line strength factors for the given detection line. Theeffect of varying k projection number is found to be negligiblefor low n, where the difference in energy between individual

k-states is small, while it is more pronounced for higher n. Anal, corrected image was then obtained by dividing the rawexperimental image by this sum of instrument functions over kprojection quantum numbers. As part of this analysis, theangular resolution of the experiment was calculated and isreported in Fig. S1 and S2 of the ESI.†

C. Rotational levels of CH3 and CD3

In this subsection, we briey describe the rotational levels of theCH3 and CD3 radicals, and their nuclear spin symmetries. Therotational energies for the lower levels of CH3 and CD3 areplotted in Fig. 3. The methyl radical is an oblate symmetric top.We use n and k to designate, respectively, the rotationalquantum number and its body-frame projection. Because thethree H (D) atoms are equivalent, the ground vibronic state ofCH3 has two nuclear spin modications, labelled ortho andpara.54,62 The ortho levels have nuclear spin symmetry A1 andinclude rotational levels for which k is a multiple of 3 (k ¼ 0, 3,6,.). In particular, the rotational levels with k¼ 0 and odd n donot exist for the ground vibronic state. The para levels havenuclear spin symmetry E and include all rotational levels forwhich k is not a multiple of 3 (k ¼ 1, 2, 4, 5, .).

The CD3 radical has three nuclear spin modications. The A1nuclear spin functions are those with rotational levels with k ¼0 and odd n and with levels for which k is a multiple of 3. The A2

Fig. 2 Newton diagram for inelastic scattering of CD3 with helium. The dis-played Newton sphere corresponds to the nk¼ 11 / n 0k0 ¼ 55 transition, for whichDE ¼ 91.3 cm�1.

Fig. 3 Rotational energy level diagrams for the ground vibrational level of the ~Xelectronic state of (a) CH3 and (b) CD3. Levels are labelled by n and (subscript)k. The colour coding identifies the different nuclear spin modifications.



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nuclear spin functions correspond to rotational levels with evenn and k ¼ 0, and also with levels for which k is a multiple of 3.Thus, rotational levels with k ¼ 3, 6, . have two components(A1 and A2). Finally, the E nuclear spin functions include alllevels for which k is not a multiple of 3.

D. REMPI detection and state distribution in incidentbeams

The distribution of rotational levels in the supersonic incidentCH3 and CD3 beams and the inelastically scattered nal levelswere detected using (2 + 1) REMPI spectroscopy through the 000band of the 4p2A

002 ) ~X

2A002 transition.63,64 Lines in the Q branch

are by far the strongest and were employed to optimize theexperimental conditions but were of no value in determiningstate-to-state DCSs because of spectral overlap.

The level distributions in the incident radical beams weredetermined by comparison of experimental spectra with spectrasimulated using the PGOPHER program.65 The simulationincorporated the effects of nuclear spin statistics of the threeequivalent H or D atoms. The procedures used are described inthe ESI,† which also contains an example spectrum (Fig. S3†).The derived relative populations are listed in Table 1 and corre-spond to a rotational temperature of 15 K. As expected from thesmaller rotational constants of CD3, more rotational levels havesignicant populations than in the CH3 isotopologue.

It should be noted that the lines in the REMPI spectrum ofmethyl are resolved in the n rotational quantum number, butnot in the k projection quantum number. Depending upon thespectroscopic branch, and hence Dn (s0) of the line used todetect the nal level, the k projection levels of a given ncontribute differently. The levels associated with the DCSsreported below are denoted by nk1k2. to indicate that theunresolved nk1, nk2, . levels have been detected on the giventransition. The relative contributions of the different k projec-tion levels to the measured REMPI intensity were determined bycalculating 2-photon line strength factors using the PGOPHERprogram.

The levels of the excited 4p2A002 electronic state are predis-

sociated, and the linewidths for the CH3 isotopologue are larger

than for CD3. Hence, the efficiency of detection of CH3 rota-tional levels is lower, and it was possible to determine DCSs forfewer nal levels than for CD3. In addition, the computedintegral cross sections for formation of higher CH3 rotationallevels were found to be smaller than for CD3 levels of compa-rable rotational angular momentum.

E. Quantum scattering calculations

We used the HIBRIDON suite of programs66 to carry out fullyquantum, close-coupled, state-resolved differential crosssection calculations for collisions of CH3 and CD3 with He. Thebulk of the calculations employed our previously computed54

PES for the interaction of CH3, xed at its equilibrium geometry,with helium. Since the centre of mass of methyl is located at thecarbon atom, this PES could be used without modication forthe CD3 isotopologue. Some additional calculations on CD3–Hewere carried out with a PES for which the CD3 geometry wasaveraged over the probability distribution for the n2 umbrellacoordinate, using our previously determined53 4-dimensionalPES involving this degree of freedom.

Rotational energies were computed with a rigid rotorsymmetric top Hamiltonian using spectroscopic studies byYamada et al.67 for CH3 and Sears et al.68 for CD3. The methylradical is an open-shell species, with doublet spin multiplicity,so that each rotational level, with rotational angularmomentum n, is split into spin doublets, with total angularmomentum j ¼ n � 1/2. We have ignored spin in our scatteringcalculations since the spin-rotation splitting and hypernesplittings are small69 and not resolved in the REMPI spectra.Separate calculations were carried out for each of the threenuclear spin modications since they are not interconverted incollisions with closed-shell species without nuclear spin.

We checked convergence of the differential cross sectionswith respect to the size of the rotational basis and the number ofpartial waves in the calculation. Rotational levels whoseenergies were less than 1100 cm�1 were included in thechannel basis, and the calculations included total angularmomenta J # 130ħ.

Since the CH3 and CD3 incident beams each containedseveral rotational levels, DCSs for formation of a specic nalrotational level nk were determined by weighting the computedstate-to-state DCSs at the experimental collision energy by theexperimentally determined rotational level populations in theincident beam, which are listed in Table 1. Since the k projec-tion number of the scattered radicals is not resolved in theREMPI spectra, theoretical DCSs for comparison with theexperimental measurements were weighted according tothe 2-photon line strength factors for the given detection line.More details can be found in ESI.†

We observed previously that CH3 + He integral cross sectionscomputed with the rigid-molecule PES were virtually identical(within 1%) to those computed using a PES in which theumbrella motion was averaged over the n2 ¼ 0 probabilitydistribution.53 We nd a similar excellent agreement of CD3 +He DCSs computed with rigid-molecule and umbrella-averagedPESs. The only exception was a slight increase (�5%) of the

Table 1 Populations (given in percent of the total population) of the CH3 andCD3 rotational levels in the incident molecular beams

a

Rotational level nk CH3 CD3

00 48.6 2.511 41.0 33.210

b 32.622 7.2 14.721 1.7 8.820 1.0 0.833 0.4 3.932 0.0 1.331 0.0 0.830

b 0.8

a These populations correspond to a rotational temperature of 15 K.b This rotational level does not exist.


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forward (q < 10�) scattering for low-Dn, Dk ¼ +3 transitions, e.g.10 / 33 as shown in Fig. S6 of the ESI.† Consequently, forcomparison with experiment we used the DCSs calculated withthe rigid-molecule PES.

ResultsA. DCSs for CD3 + He collisions

From the measured beam speed distributions (see ESI†), themean CD3 + He collision energy was calculated to be 440 cm

�1

with an expected spread of �35 cm�1. Fig. 4 presents the rawimages recorded for detection of CD3 nal rotational levels forn0 ¼ 2–9. These images were each typically accumulated for 8 to10 hours. The scattered products cannot be observed in theportions of the images corresponding to the forward directionbecause of imperfect subtraction of background signals arisingfrom unscattered CD3 radicals present in the parent molecularbeam. The incomplete cooling of the methyl radicals to the

lowest rotational level of a given nuclear spin modicationduring the supersonic expansion is the origin of this masking ofthe scattering signals and is more signicant when lower rota-tional levels are probed. Nevertheless, from examination of theimages, we see that the scattering is conned relatively close tothe incident beam direction for detection of low n0 nal levels.This suggests that the scattering is largely in the forwarddirection for these levels. By contrast, signicant intensityextends to a much larger range of scattering angles for high n0

nal levels.The recorded images were analysed following the procedures

described in Method Section B to correct for the density-to-uxtransformation in order to derive the DCSs. Fig. 5 displays thedetermined DCSs for nal levels n0 ¼ 2–4, while Fig. 6 presentsthe DCSs for n0 ¼ 5–9. In both gures, the unresolved k0projections are specied for each n0 – resolved DCS. Also shownin Fig. 5 and 6 are theoretical DCSs. The experimental DCSs arenot shown for q < 30� for nal levels with n0 ¼ 2 and 3 and for q <20� for nal levels with higher n0 because of contributions tothese angles from unscattered radicals in the parent beam, asdiscussed above. The calculated DCSs show pronounced

Fig. 4 Raw images for inelastic scattering of CD3 radicals by He at a collisionenergy of 440 � 35 cm�1. The images are denoted by the symbol Yðn0k01�k0N Þ forfinal rotational levels from n0 ¼ 2–9, with unresolved final k0 projection levels asdiscussed in the text. Y denotes the spectroscopic branch. The rotational angularmomentum of the incident CD3 beam was predominantly n ¼ 1 (see Table 1 forthe complete incident level distribution). The orientation of the relative velocityvector vrel is indicated in one panel.

Fig. 5 DCSs for inelastic scattering of CD3 radicals by He at a collision energy of440 � 35 cm�1 into final rotational levels n0 ¼ 2–4. The REMPI line employed fordetection is indicated, along with the range of k0 projection levels contributing tothe scattering. Red curves: DCSs determined from the measured images displayedin Fig. 4; black curves: theoretical DCSs computed as described in MethodSection E. The method of normalization of the experimental DCSs is described inthe main text.



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diffraction oscillations in this strongly forward scattered region.Unfortunately, even with greater initial state purity the angularresolution of the experiments, imposed by the velocity andangular spreads of the two molecular beams, would be insuffi-cient to resolve these structures clearly. For the current experi-ments on the CD3 + He system, this angular resolution rangesvaries from 3 to 16� depending on the scattering angle (see ESI†for further details).

For quantitative comparison with the theoretical calcula-tions, the experimental angular distributions are normalized byscaling the experimental value to match the theoretical value ateither 90� for levels with n0 # 4, or at 180� for higher n0 states.These choices were made to ensure that the comparison wasdone at angles where the experimental signal levels werestrongest. The error bars associated with the experimental DCSs

were determined by combining the standard deviation deter-mined from comparison of several (typically 3) measuredimages for a single nal state with the uncertainty introducedby application of the density-to-ux transformation. The latterfactor was quantied by comparing DCSs extracted from the twohalves of the image separated by the relative velocity vector(which should be symmetric aer perfect transformation). Thetheoretical DCSs reproduce satisfactorily all the features of themeasured DCSs to within the experimental uncertainty. Then0-dependent DCSs are a sensitive probe of both attractive andrepulsive parts of the potential. The near quantitative agree-ment for all nal n0 levels conrms the high quality of thecalculated ab initio PES54 and the accuracy of the close-couplingtreatment of the scattering dynamics.

In most cases, different spectroscopic branches can be usedto detect a given methyl rotational level n0. The unresolved k0

projections of the given n0, weighted according to the 2-photonline strength factors (see Method Section D) will give rise toslightly different predicted DCSs. As an illustration of thissubtle effect, we see in Fig. 5 and 6 that the experimental andtheoretical DCSs for a given n0 are slightly different for detectionof this level on REMPI lines of different Dn0. This is mostdramatically illustrated in Fig. 5 in the comparison of detectionof n0 ¼ 4 on theO(4), P(4), and S(4) lines. The differingmeasuredDCSs reect the fact that the k0 projection levels of nal rota-tional level n0 ¼ 4 have different DCSs. This point will be takenup again in the Discussion.

B. DCSs for CH3 + He collisions

The collision energy of 425 � 35 cm�1 for inelastic scattering ofCH3 radicals (seeded in excess Ar) with He is slightly smallerthan for the scattering of CD3 by He, because of the smallerreduced mass. The spectroscopic lines for CH3 are also notresolved in the k projection quantum number, although thespacings between the lines detecting different k levels of thesame n are larger than for CD3. In addition, the CH3 REMPItransitions are more broadened by predissociation of theintermediate Rydberg state, which lowers the detection effi-ciency. Consequently, velocity map images for CH3 scatteringwere recorded only for the three strongest spectroscopic lines.

Fig. 7 presents representative examples of these images. TheDCSs derived from the density-to-ux transformation (MethodSection B) and normalized to the theoretical DCSs are presentedin Fig. 8. In two of the panels in Fig. 8, experimental DCSsderived from images accumulated on different days arecompared. We see that these DCSs lie almost entirely on top ofeach other, which demonstrates excellent reproducibility. Fig. 8also compares these experimental DCSs with theoretical calcu-lations. There is agreement for the n 0k0 ¼ 3123 and 21 nal levels,except for small angle scattering. However, the experimentalDCS for scattering into n 0k0 ¼ 2012 does not agree with thecomparable theoretical DCS for q # 90�, computed under theassumption that the probe laser excites all three k0 projectionlevels. Re-measurement of the images conrms the reproduc-ibility of the experimentally determined DCSs (red and bluelines in Fig. 8b). However, careful examination of the 2-photon

Fig. 6 DCSs for inelastic scattering of CD3 radicals by He at a collision energy of440 � 35 cm�1 into final rotational levels n0 ¼ 5–9. The REMPI line employed fordetection is indicated, along with the range of k0 projection levels contributing tothe scattering. Red curves: DCSs determined from the measured images displayedin Fig. 4; black curves: theoretical DCSs computed as described in Method SectionE. The normalization of the experimental DCSs is described in the main text.



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transition wavenumbers reveals that lines originating fromthese k0 levels are separated by more than their widths. If weassume that the k0 ¼ 2 level was preferentially excited, then weobtain good agreement of the computed DCS [green curve inFig. 8b] with the experimental DCS.

Discussion

The agreement between the measured and calculated DCSs forscattering of both CH3 and CD3 radicals with He at respectivecollision energies of 425 and 440 cm�1 lends considerablecondence to the quality of the theoretical treatment outlinedin Method Section E. We can therefore derive insights into thescattering dynamics not only from comparison with experiment

(as we have done in the case of Fig. 5, 6 and 8), but also byanalysis of the calculated, fully state resolved DCSs.

The raw experimental images immediately reveal a trendthat is borne out by the derived DCSs and by the scatteringcalculations: for both CD3 or CH3 the angular distributions fortransitions into n0 ¼ 2–4 (averaged over k0), where the degree oftranslational to rotational energy transfer is small, peak in theforward hemisphere, whereas those with n0 $ 5 (i.e. interme-diate to large energy transfer) are predominantly sideways andbackwards scattered. The degree of backward scatteringincreases steadily with increasing n0, and hence with Dn,because the initial levels of CD3 populated have mostly n ¼ 1(Table 1).

Similar behaviour is observed in the inelastic scattering ofatoms such as He with diatomic molecules,19,22,23 and revealsthat low impact parameter collisions (with, presumably, largerangles of deection) are necessary for large changes in therotational angular momentum. Classically, the rotationalangular momentum of the molecule is induced by a torque thatacts on the molecule for the duration of the collision.70 Themagnitude of the torque is proportional to the gradient of theintermolecular potential, which is largest at short range.

Beyond the Dn dependence of the DCSs, we can also explorethe efficiency of changes in the projection quantum number k.The experimental DCSs determined using CD3 REMPI linesoriginating from the same n0 level but corresponding todifferent spectroscopic branches probe different groups of k0

projection quantum numbers. Thus, as highlighted earlier,Fig. 5 illustrates the DCSs for transition into n0 ¼ 4 obtained byO(4), P(4) and S(4) transitions, which probe, respectively, k0

projections 0–2, 1–3, and 0–4. The varying DCSs obtainedindicate clearly that there is a signicant variation with k0. Thecalculations reveal the fully k0-resolved dependence: compare,for example, the 11 / 41, 42 and 44 DCSs displayed in Fig. 9 forscattering of both CH3 and CD3.

In the previous theoretical study,54 the 3-fold corrugation ofthe PES resulting from repulsion of the helium atom by thethree H atoms on the methyl radical gave rise to a strong

Fig. 7 Raw images for inelastic scattering of CH3 radicals by He at a collisionenergy of 425 � 35 cm�1. The images are denoted by the symbol Yðn0k01.k0N Þ forfinal rotational levels with n0 ¼ 2 and 3 and unresolved final k0 projection levels asdiscussed in the text and shown with each image. Y denotes the spectroscopicbranch. The rotational angular momentum of the incident CH3 beam waspredominantly n ¼ 0 and 1 (see Table 1 for the complete incident level distri-bution). The orientation of the relative velocity vector vrel is indicated in one panel.

Fig. 8 DCSs for inelastic scattering of CH3 radicals by He at a collision energy of425 � 35 cm�1 into final rotational levels n0 ¼ 2 and 3. The REMPI line employedfor detection is indicated, along with the range of k0 projection levels contributingto the scattering. Panels (b) and (c) also compare experimental DCSs for repeatmeasurements made on different days to demonstrate the reproducibility of theexperimental determinations.

Fig. 9 Theoretical state-to state CH3/CD3 + He inelastic DCSs out of the level nk =11 into levels with n0 = 4, at a collision energy of 425/440 cm

�1.



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propensity for Dk ¼ �3 in the integral CH3 + He inelastic crosssections. To illustrate this corrugation, Fig. 10 presents theatom–molecule separation R at which the interaction energy isequal to 440 cm�1 (the collision energy) as a function of theangles (qHe, fHe) that dene the orientation of the He atom (seeFig. 1 of ref. 54). The heavy line in Fig. 10 shows the 3-foldcorrugation of the PES for approach of the He atom in themolecular plane.

It is also interesting to ask how the periodic corrugation ofthe PES might be manifested in the angular dependence of thestate-to-state scattering. Fig. 11 presents computed state-to-state DCSs for scattering of the lowest rotational levels of eachnuclear spin modication of CH3 and CD3 into the n0 ¼ 2 and 3nal rotational levels. The sums of such DCSs weighted by thedistribution of populations over initial CD3 or CH3 levels givenin Table 1, but resolved by nal n0 and k0 level, are plotted in theESI† section. The DCSs plotted in Fig. 11 for the same initial

rotational level of the two isotopologues are similar. Conse-quently, we henceforth concentrate on the CD3 isotopologue.

The DCSs for all Dk ¼ 0 transitions have a similar shape,namely a reasonably sharp forward peak and a broad, lowerintensity peak in the backward hemisphere. These transitionsin all the nuclear spin modications are induced primarily bythe v20 term in the expansion of the PES.54 By contrast, the|Dk| s 0 transitions all display a broad DCS, starting from zerointensity at q ¼ 0� and extending over the entire angular range,with oscillations at small angles (q # 45�). In the case of thelevels of A1 and A2 nuclear spin symmetry, these transitionsinvolve Dk ¼ 3 and are enabled by the strong v33 term in theangular expansion of the PES, as discussed previously in somedetail.54 For the levels of E symmetry, many Dk ¼ 1 transitions,e.g. 11 / 22, can be described as a Dk ¼ �3 transition from thek ¼�1 component of the initial level to the k0 ¼H2 componentof the nal level.54 Again, this transition is enabled by the v33term. Hence, for the low Dn, Dk s 0 transitions, the shapes ofthe DCSs are closely connected with the change in the kprojection quantum number in the collision.

To gain further insight into the origin of the differences inthe DCSs for Dk ¼ 0 vs. �3 transitions, we can consider thedependence of the scattering upon the impact parameter. Sincethe initial and nal rotational quantum numbers n and n0 aresmall compared to the orbital angular momentum L, the orbitalangular momentum is approximately equal to the total angularmomentum J. The partial cross sections (the contribution to theICS from each value of J) give information about which range ofimpact parameters contributes to a particular transition. Fig. 12presents a plot of the partial cross sections from the 10 level tothe 30 and 33 levels, and to the higher 50 and 66 levels. The

Fig. 10 Atom–molecule separation (in bohr) at which the CD3–He interactionenergy equals the (440 cm�1) collision energy. The angular coordinates aredefined in Fig. 1 of ref. 54. The heavy line indicates the direction of approach ofthe atom within the molecular plane.

Fig. 11 Theoretical state-to state DCSs for inelastic scattering of CH3 and CD3with He out of the lowest rotational levels of each nuclear spin modification, atrespective collision energies of 425 and 440 cm�1.

Fig. 12 Partial cross sections for CD3 + He collisions at 440 cm�1 for scattering

from the nk ¼ 10 initial level.



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scattering into both n0 ¼ 3 nal levels is dominated by the samerange of J (i.e., classically, by the same range of impact param-eters), but the partial cross sections for the 30 level exhibit abimodal distribution peaking at J ¼ 16 and 33. The high-J andlow-J peaks are related to the strong forward and backwardpeaks seen in the DCS for this transition. In contrast, the partialcross sections for the 33 level display a single peak at J ¼ 22.Similarly, for this transition, only a single broad peak appears inthe DCS. Also, we observe that the scattering into the higherrotational levels, exemplied here by the 50 and 66 levels, occursat smaller values of J (i.e. impact parameters). The torquerequired for a large Dn transition requires a hard collision atsmall impact parameters.

Since the contribution to the integral cross sections into the30 and 33 levels occurs over the same range of impact parame-ters, it is not possible to use the partial cross sections to explainfully the difference in the DCSs for these two levels. Possibly, theorientation of the CD3 molecule plays a signicant role. Therotational angular momentum of the CD3 molecule in the 33level is oriented along the C3 symmetry axis, so that the mole-cule is rotating perpendicular to this axis. Excitation of thisrotational motion will be most readily induced by a collision inwhich the He atom approaches in the plane of the three D (orthree H) atoms (i.e. qHe z 90� in Fig. 10). In contrast, in the 30level the CD3 molecule rotates about an axis perpendicular tothe C3 symmetry axis. Excitation of this motion will require acollision with a He atom approaching out of the hydrogenicplane (i.e. qHe away from 90� in Fig. 10).

For all nal levels measured, the experimental DCSs forinelastic scattering of CD3 are somewhat more forward peakingthan those for CH3 (see Fig. S7 of ESI† for direct comparisons).As mentioned above and shown in Fig. 9, the state-to-state DCSsof the two isotopologues are, however, very similar. The differ-ences in the measured DCSs may be explained by consideringthe initial level population in the primary molecular beam. Forthe CH3 radical the 10 level is missing, and the 00 level is themost populated, whereas for CD3 the most populated levelshave n¼ 1. Accessing a particular nal n0 level therefore involvesa smaller Dn0 for CD3 than in the case of CH3.

Fig. 13 shows theoretical DCSs for inelastic scattering of CD3out of the various k ¼ 1 and 2 rotational levels with n ¼ 1–3 intolevels with n 0k0 ¼ 44 and 55. Different behaviour is seen, as afunction of the initial rotational angular momentum k of theCD3 molecule. For the 44 nal level, the DCSs for k ¼ 1 initiallevels peak in the forward hemisphere, while those for k ¼ 2peak in the backward hemisphere. The former and latter involveDk ¼ 3 and 6 transitions (the latter probably involving twovirtual Dk ¼ 3 transitions), respectively. The situation for the 55nal level is reversed; in this case, transitions out of the k ¼ 1and 2 initial levels involve Dk¼ 6 and 3 transitions, respectively.

Fig. 14 displays theoretical state-to-state DCSs for inelasticscattering of CD3 out of the nk ¼ 11 rotational level into k0 ¼ 1rotational levels with n0 ¼ 2–7. These Dk ¼ 0 collisions induceadditional rotation about an axis perpendicular to the C3symmetry axis but do not change the projection k of the rota-tional angular momentum along the symmetry axis. The cor-responding DCSs provide insight into which collisions lead to a

change in the magnitude of n while preserving its componentalong the C3 axis. We observe that as n0 (and hence Dn)increases, the bimodal distribution present for the 21 and 31nal levels develops into a single peaked backward distribution.

We can also explore the dependence of scattering on theinitial angular momentum by comparison of the dependenceon n of state-to-state DCSs for a xed increase in n. Fig. 15 showstheoretical state-to-state DCSs for inelastic scattering of CD3 byHe for Dk ¼ 0 transitions involving different k ¼ 1 initial levelsand Dn ¼ 1. When normalized to the maximum value, the DCSsappear remarkably similar. There is very little sensitivity to theinitial level, even though the energy transfer associated withthese transitions is larger for higher initial n, as can be seen inTable 2.

The comparisons made in Fig. 9 and 11–15 are far fromexhaustive, but provide examples of insights that can be drawnfrom the state-to-state DCSs. They illustrate the consequence of

Fig. 13 Theoretical state-to state DCSs for inelastic scattering of CD3 with He outof several initial rotational levels into the n 0k0 ¼ 44 and 55 final levels, at a collisionenergy of 440 cm�1.

Fig. 14 Theoretical state-to state DCSs for inelastic scattering of CD3 with He outof the nk ¼ 11 level into rotational levels with k0 ¼ 1, but with varying n0 at acollision energy of 440 cm�1.



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the angular periodicity in the PES, and the additionalcomplexity that arises when the collision partner is nonlinear.

Conclusions

We have presented an in-depth comparison of differential crosssections for rotationally inelastic scattering of methyl radicals(both CH3 and CD3) with He. The measurements made use of anewly constructed crossed molecular beam and velocity mapimaging instrument. The results presented here represent (toour knowledge) the rst reported determinations of DCSs forinelastic scattering of a polyatomic free radical. The agreementis excellent with the predictions of close-coupling scatteringcalculations on a recently reported ab initio potential energysurface. CD3 radical scattering was examined for nal n0 levelsup to n0 ¼ 9 in the vibrational ground state, whereas experi-ments for CH3 radicals were limited to n0 ¼ 2 and 3. Because oflimitations in the REMPI detection scheme, the CM-frameexperimental angular distributions represent sums over anunresolved group of k0 projection levels.

The accuracy of the calculated, fully state-resolved state-to-state DCSs out of initial states with nk ¼ 00 and 11 is conrmedby comparison with the less highly resolved experimental data.The theoretical calculations also allow an instructive study ofhow the features of the underlying PES inuence the relativemagnitude of the differential scattering into various n0 and k0

nal states.

The excellent agreement between theory and experiment isvery satisfying, but limited (so far) to the single collision energyused here, and to the use of He as a single collision partner. Weare initiating comparable experimental and theoretical studiesof the scattering of methyl radicals with Ar, H2 and D2 toascertain whether we can achieve a comparable level of agree-ment and understanding for collisions of CD3 (CH3) withheavier or more structurally complicated collision partners.

Acknowledgements

The Bristol group acknowledges nancial support from theEPSRC Programme Grant EP/G00224X and from the EU MarieCurie Initial Training Network ICONIC (for an Early CareerResearcher position for OT). We thank Dr Kevin E. Strecker andDr David W. Chandler (Sandia National Laboratory, Livermore)for inspiring the construction of the crossed molecular beamand velocity map imaging instrument, and for valuablediscussions about its design. We are grateful to Dr C. M.Western (University of Bristol) for assistance with the PGOPHERsimulation of methyl radical REMPI spectra. SJG thanks EPSRCfor award of a Career Acceleration Fellowship EP/J002534/2. Thetheoretical portion of this work was supported by the Chemical,Geosciences and Biosciences Division, Office of Basic EnergySciences, Office of Science, U.S. Department of Energy, underGrant no. DESC0002323.

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Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...

Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...

Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging data with quantum scattering calculationsElectronic...

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Rotationally inelastic scattering of CD 3 and CH 3 with He Tká, … · 2015. 5. 31. · Rotationally inelastic scattering of CD3 and CH3 with He: comparison of velocity map-imaging